International Journal of Dynamics and Control https://doi.org/10.1007/s40435-019-00531-y Complex dynamics from a novel memristive 6D hyperchaotic autonomous system Brice Anicet Mezatio 1,2 · Marceline Motchongom Tingue 3 · Romanic Kengne 1,2 · Aurelle Tchagna Kouanou 2 · Theophile Fozin Fonzin 2 · Robert Tchitnga 1,2 Received: 30 November 2018 / Revised: 20 February 2019 / Accepted: 14 March 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019 Abstract A simple 5D hyperchaotic system recently introduced in the literature is modified by using a charge-controlled memristor model and striking behaviors are uncovered. The resulting system is a 6D hyperchaotic system, which generates hidden attractors with the unusual feature of having plan and line equilibrium under different parameter conditions. Its dynamical behaviors are characterized through bifurcation diagrams, Lyapunov exponents, phase portraits, Poincaré sections and time series. Rich nonlinear dynamics such as limit cycles, quasi-periodicity, chaos, hyperchaos, bursting and hidden extreme multistability are found for appropriate sets of parameter values. The high complexity of the system is confirmed by its Kaplan–yorke dimension (greater than five). Additionally, an electronic circuit is designed to implement the novel system and PSpice simulation results are in good accordance with the numerical investigations. To the best of our knowledge, this system is the first with higher order presenting all those phenomena. Keywords 6D hyperchaotic system · Hidden extreme multistability · Bursting oscillations · Offset boosting 1 Introduction An article [1] by Leon Chua appeared in 1971, presenting the logical and scientific basis for the existence of a fourth fun- damental circuit element called the memristor (a contraction for memory resistor); resistor, inductor, and capacitor being the three others. However, memristor was largely ignored by the scientific community until the seminal publication by Strukov and co-workers announcing that the missing circuit element has been found [2]. After this first memristor from HP (Hewlett Packard) laboratories, many others have been fabricated [3–7]. Sine then, though memristor is yet to be B Romanic Kengne kengneromaric@gmail.com 1 Research Group on Experimental and Applied Physics for Sustainable Development, Department of Physics, Faculty of Science, University of Dschang, P.O. Box 412, Dschang, Cameroon 2 Unité de Recherche de Matière Condensée d’Electronique et de Traitement du Signal (URMACETS), Department of Physics, Faculty of Science, University of Dschang, P.O. Box 67, Dschang, Cameroon 3 Higher Technical Teachers Training College, University of Bamenda, P.O. Box 39, Bambili, Cameroon commercially available, emulator memristors are often used to explore applications in science and engineering. Mem- ristors can be used as synapses in neuromorphic circuits [8]; memristive devices have been studied as promising candidate for emerging non-volatile memory technology [4,6]. In addi- tion, they have now been widely adopted to produce complex dynamics, because of their nonlinearity and memory ability. These include multistability [9–15] and hidden extreme mul- tistability [16–18]. Appropriate definition of hidden attractors can be found in relevant literature [19–22]. Roughly speaking, they occur in dynamical systems without any equilibrium points [17,23]; with only stable equilibria [24] or infinite equilibrium points [25–28]. However, hidden attractors are important in engi- neering applications because they allow unexpected and potentially disastrous responses to perturbations in a struc- ture like a bridge or an airplane wing [26]. Furthermore, coexistence of different kinds of hidden attractors as the initial condition of a certain state variable changes(hidden multistability) yields more uncertainty; specially when the number of coexisting attractors tends to infinite, a phe- nomenon known as hidden extreme multistability. A char- acteristic which is useful in cryptography and many other chaos based applications. As a matter of fact, analysis of 123